LSR-Net: Learning the Forward Evolution Operator for Nonlinear Fluid Dynamics
Abstract
We introduce the Long-Short-Range Neural Network (LSR-Net), a novel neural operator architecture designed for data-driven forward evolution modeling, and extends it to the prediction of nonlinear fluid dynamics. LSR-Net learns the evolution operator of a dynamical system solely from pairs of initial and future state snapshots, which splits the learnable integral kernel into long-range (LR) and short-range (SR) components within stacked network blocks. While the SR component uses standard convolutions to capture local dynamics, the LR component employs a sum-of-exponentials (SOE) representation. This allows for the efficient computation of global interactions as a trainable Fourier multiplier, reducing computational complexity to O(n log n) where n is the number of pixels in an input snapshot and requiring only a few parameters per channel. LSR-Net is evaluated on three challenging 2D benchmarks: the coupled Burgers equation, the wave equation with a spatially varying coefficient, and the nonlinear shallow water equation {(SWE)}. Results demonstrate that LSR-Net significantly outperforms the baseline short-range network (SR-Net) as well as FNO and DeepONets in predictive accuracy, achieving substantially lower relative errors by effectively capturing both local fine-scale structures and crucial global pattern interactions.
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BibTeX
@misc{hou2026lsrnet,
title = {{LSR-Net: Learning the Forward Evolution Operator for Nonlinear Fluid Dynamics}},
author = {Qian Hou and Sutrisno and Yuqing Li and Zecheng Gan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19039},
eprint = {2609.19039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19039},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - LSR-Net: Learning the Forward Evolution Operator for Nonlinear Fluid Dynamics
AU - Qian Hou
AU - Sutrisno
AU - Yuqing Li
AU - Zecheng Gan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.19039
UR - https://arxiv.org/abs/2609.19039
AB - We introduce the Long-Short-Range Neural Network (LSR-Net), a novel neural operator architecture designed for data-driven forward evolution modeling, and extends it to the prediction of nonlinear fluid dynamics. LSR-Net learns the evolution operator of a dynamical system solely from pairs of initial and future state snapshots, which splits the learnable integral kernel into long-range (LR) and short-range (SR) components within stacked network blocks. While the SR component uses standard convolutions to capture local dynamics, the LR component employs a sum-of-exponentials (SOE) representation. This allows for the efficient computation of global interactions as a trainable Fourier multiplier, reducing computational complexity to O(n log n) where n is the number of pixels in an input snapshot and requiring only a few parameters per channel. LSR-Net is evaluated on three challenging 2D benchmarks: the coupled Burgers equation, the wave equation with a spatially varying coefficient, and the nonlinear shallow water equation {(SWE)}. Results demonstrate that LSR-Net significantly outperforms the baseline short-range network (SR-Net) as well as FNO and DeepONets in predictive accuracy, achieving substantially lower relative errors by effectively capturing both local fine-scale structures and crucial global pattern interactions.
ER -